The Kähler-Ricci flow on pseudoconvex domains

Abstract

We establish the existence of Kähler-Ricci flow on pseudoconvex domains with general initial metric without curvature bounds. Moreover we prove that this flow is simultaneously complete, and its normalized version converge to the complete Kähler-Einstein metric, which generalizes Topping's works on surfaces.

17 pages, Theorem 1.3 is strengthened and combined to Theorem 1.2